General Motors Corp (GM.N: Quote, Profile, Research, Stock Buzz) will close more U.S. plants and cut more jobs and still faces a higher probability of bankruptcy to shed debt, GM Chief Executive Fritz Henderson said on Tuesday.

The expectation is that we need to go deeper, Henderson said in describing GM's restructuring after its previous plan was rejected as insufficient by U.S. officials.

We need to go deeper and we need to go faster, he said in a news conference at GM's Detroit headquarters that included reporters on a conference call.

The appearance was the first since Henderson took over as chief executive of the embattled automaker on Monday.

His predecessor, Rick Wagoner, was forced out by the Obama administration, which gave GM 60 days to reach deeper concessions with bondholders and the United Auto Workers union and said it would finance a court-supervised bankruptcy if the process failed to deliver deep enough savings.

Henderson said GM could decide to file for bankruptcy within its 60-day deadline if it became quite clear that it would be unable to reach the deals it is seeking.

By no later than June 1, if we're not able to accomplish this outside bankruptcy, we'll be in bankruptcy. It's pretty clear. The government was unequivocal, he said.

Henderson said the autos task force headed by former investment banker Steve Rattner has not given GM new targets for slashing debt from its balance sheet.

But officials made it clear that GM would have to bring its structural costs below $26.3 billion in 2009 and cut its unsecured debt by more than $28 billion, he said.

Both of those targets had been established by the GM plan that U.S. officials said did not go far enough to restoring the No. 1 U.S. automaker to a strong financial footing.

What they said was that they want us to have a clean balance sheet, a healthy balance sheet and one that allows us to be competitive going forward, Henderson said.

Henderson said GM would revise its restructuring plan to account for the risk of lower sales.

The White House-appointed autos panel said the automaker had been overly optimistic in projecting that it could hold market share steady near 22 percent after decades of declines.

As a result, GM will need to close more than the five plants it had identified in February and will have to return to the UAW to offer another round of buyouts to factory workers.

I would expect that we would need to take further measures, Henderson said.

Last week, GM announced that 7,500 UAW workers -- or about 12 percent of its U.S. factory workforce -- had accepted early retirement or buyout offers to leave the payroll.

GM has cut 60,500 jobs -- or more than half of its factory workers -- over the past three years as sales have slowed and its financial position has weakened.

(Reporting by Kevin Krolicki; Editing by Phil Berlowitz)